To find the limit of the function as x approaches 2, we can first simplify the function by factoring out an x^2 from the numerator and denominator:

(x^3 - 3x^2 + 4) / (x^4 - 4x^2)
= x^2 (x - 3 + 4/x^2) / x^2 (x^2 - 4)

Now we can cancel out the common x^2 terms in the numerator and denominator:

= (x - 3 + 4/x^2) / (x^2 - 4)

Next, substitute x = 2 into the simplified function:

(2 - 3 + 4/2^2) / (2^2 - 4)
= (2 - 3 + 4/4) / (4 - 4)
= (-1 + 1) / 0
= 0 / 0

Since we obtained an indeterminate form of 0 / 0, we can further simplify the function by factoring out the common (x - 2) term in the numerator:

= [(x - 2) - 1 + 4/x^2] / (x + 2)(x - 2)

Now, substitute x = 2 into the simplified function:

= [(2 - 2) - 1 + 4/2^2] / (2 + 2)(2 - 2)
= (0 - 1 + 1) / (4)
= 0

Therefore, the limit of the function as x approaches 2 is 0.